Separating and pooling equilibria in Akerlof model

Player 1 first observes the quality (q) of the indivisible good he owns
before proposing a price (p) at which he will sell the good to Player 2,
who responds to the offer by either accepting or rejecting. Trade takes
place at a price of p if Player 2 accepts; otherwise no trade takes place.
Player 1's payoff equals the revenue (p or 0) he receives, irrespective of
quality; Player 2's payoff equals q &#8722; p if trade takes place, and otherwise
equals 0. Quality can take two values, L and H, where H > L > 0, and is
equally likely to take each value. Describe all separating and all pooling
equilibria of this game.

Solution Preview

A pooling equilibrium occurs when different types all choose the same message. A separating equilibrium occurs when different types choose different messages. In this case, sellers can send messages through price. A higher price should indicate a high quality, since high quality goods are worth more. A lower price indicates a lemon. However, a pooling equilibrium will occur if both types of sellers choose the same price. Buyers then offer an average price, based on the probability of the product being a lemon.